Conventional methods for determining the strength of concrete placed into a structure require casting, curing and breaking test specimens. The specimens, typically cured at a constant temperature in a 100% humidity environment, are assumed to be representative of the concrete in the structure itself. However, the curing conditions for the concrete within the structure are rarely, if ever, the same as the conditions seen by the test specimens. Furthermore, conventional methods for estimating the compressive and/or flexural strengths of concrete are expensive and lack the desired levels of precision often required for quality control and acceptance applications.
The maturity method for estimating concrete strength produces an estimate of strength based on the actual temperature history experienced by the in-place concrete. As such, the maturity method attempts to reduce the incongruity resulting from differing hydration rates experienced by lab-cured specimens compared to the in-place concrete. Even so, the maturity method requires development of a strength-maturity relationship curve (also called a calibration curve) that is specific to the mixture components contained in the calibration test batch. Any significant change in the relative amounts of the individual mixture components can render the calibration curve biased or unreliable.
The use of maturity methods as a means for concrete quality control and acceptance will be hindered until methods are demonstrated to adequately and easily account for the variations in mixture components that commonly occur between various concrete batches under normal field conditions. Air and water content represent two concrete mixture components that [1] greatly influence the final strength of the concrete and [2] can vary considerably from batch-to-batch, day-to-day and week-to-week even for a given concrete mix design.
Brief History of the Maturity Method
The maturity method for measuring concrete strength has been in use for over fifty years and became an ASTM (American Society for Testing and Materials) standard in 1987 (ASTM C 1074). The heart of the method lies in the scientific relationship between chemical reaction rates and the energy (i.e. temperature) of the molecules involved in the reaction. Almost without exception, chemical reactions proceed more quickly at elevated temperatures. The application of this law to the complex chemical reactions in concrete has been demonstrated time and again both in the laboratory and the field over the past fifty years. A tragic display of this phenomenon occurred in 1973 in Fairfax County, Virginia when a multi-story building collapsed during construction, killing fourteen and injuring 34. The National Bureau of Standards (NBS) investigated the accident at the request of the Occupational Safety and Health Administration (OSHA). NBS investigators identified a four-day-old floor slab (which had been subjected to an average ambient temperature of only 7° C.) as the most likely cause of the accident (Carino and Lew 2001). This disastrous result of the temperature-dependence of concrete strength gain and a similar accident in 1978 sparked serious examination of available methods for estimating the in-place strength of concrete during construction. As a result, the NBS identified the maturity method as a viable means for estimating the strength of concrete subjected to different curing temperatures (Carino and Lew 2001). This, in turn, led to the establishment of one of the world's first standard (ASTM C 1074) for estimating concrete strength via the maturity method. As a part of the Strategic Highway Research Program (SHRP) in the mid-1990s, the Federal Highway Administration (FHWA) recommended maturity as an available technology for estimating in-place concrete strength development in highway structures (Carino and Lew 2001). The FHWA now routinely demonstrates the application of the concrete maturity method to interested federal, state and local transportation personnel via their Mobile Concrete Laboratory.
Benefits of Using Maturity Methods
The maturity method for measuring concrete strength delivers the following benefits:                a) Provides a better representation of in-place concrete strength gain than laboratory or field-cured specimens.        b) Enables any-time in-place strength measurements.        c) Provides better timing for strength-dependent construction activities.        d) Saves time and money compared to conventional strength-testing procedures.        e) Enables in-place measurements at “lowest strength” locations.        f) Enables in-place strength measurements at “critical stress” locations.        
Concerning the representation of in-place concrete strengths, the Federal Highway Administration (FHWA 1988) determined that even field-cured specimens do not accurately reflect the true rate of hydration experienced by the concrete in a structure. Hossain and Wojakowski (1994) also observed significant differences in hydration rates between in-place concrete and field-cured beam specimens. These inaccuracies are then amplified when laboratory-cured rather than field-cured specimens are used to estimate in-place concrete strength. In fact, even core specimens drilled directly from the structure do not accurately represent the strength of the concrete in the structure. The American Concrete Institute (ACI) acknowledges this fact in their well-known building code for concrete construction (ACI 318). ACI 318 recommends strength acceptance of concrete if the average of three drilled cores meets or exceeds 85% of the specified strength as long as no single core falls below 75% of the required strength. In summary, when adequate process control measures are in place for the concrete batching operations, maturity represents one of the best available method for measuring the in-place strength gain for a concrete structure.
In addition, the maturity method enables the Contractor and/or Engineer to measure strength within a structure at any time and as many times as necessary until the desired strength is achieved. Conventional strength-estimation methods require the destructive testing of cylinder, beam or core specimens and, as such, are subject to a serious “Catch-22.” If all the specimens are tested too early (i.e. the measured strength is still too low), no specimens will be available to measure strength at a later time. If the specimens are tested too late (i.e. the measured strength is much higher than required), valuable construction time has been lost. This problem can be alleviated by producing extra test specimens (e.g. two or three times as many) to make sure enough specimens are available at just the right time. Casting, curing and testing extra specimens is obviously expensive and time consuming. By far, the better solution involves the use of maturity to provide any-time measurements for in-place concrete strengths.
Because the maturity method provides a better representation of the in-place strength gain for a concrete structure and can be measured at any time, better timing can be applied to construction activities that are dependent upon the concrete having attained certain minimum strength values (e.g. post-tensioning, cutting pre-stress tendons, removing formwork/falsework, backfilling, etc.). This improved timing results in maximum time savings without sacrificing safety or quality.
Given the high cost of user delays and contract overhead, the financial savings resulting from the improved timing of construction activities is sizeable. Furthermore, additional financial savings result from the reduced number of test specimens required when maturity methods are appropriately utilized. Concerning the potential savings from the use of maturity methods, the Federal Highway Administration (Crawford 1997) states,                “The maturity method is a useful, easily implemented, accurate means of estimating in-place concrete strength. . . . In a time when public agencies and contractors are concerned with escalating costs and shrinking budgets, this method provides a viable means of reducing costs through testing and scheduling. Also, quality assurance costs can be reduced because the number . . . of test cylinders is reduced by using the maturity concept.”        
Given the fact that concrete subjected to higher temperatures will gain strength faster than concrete cured at lower temperatures, the concrete within a structure will gain strength at different rates in different locations depending upon the different temperature conditions within the structure. For instance, thinner sections will tend to generate and retain less internal heat than will adjacent sections containing more mass and/or less surface area. Similarly, portions of a structure (particularly pavement structures) can gain strength at different rates due to the effects of shading and/or direct sunlight. The maturity method for measuring in-place concrete strength enables the interested parties to take measurements at locations where the strength gain is likely to be slowest, providing additional assurance that subsequent work does not begin until adequate strength has been gained within the entire structure.
In addition, this “pinpoint” capability of measuring strength via maturity allows the engineer to specifically target strength measurements in those locations where critical stresses are expected for the anticipated loading conditions during subsequent construction activities.
Hydration of the cementitious reaction products in concrete requires water as the complementary reactant. Whereas water represents one of the major constituents of fresh concrete, the initial water within the concrete mass ignites the initial hydration reactions and allows the hydration reactions to continue until the water and/or the cementitious reaction products are completely used up. As such, the ongoing cementitious hydration of concrete tends to desiccate the concrete over time. Further loss of internal moisture in the concrete due to evaporation from the surface tends to result in drying-shrinkage cracks in the concrete mass. In addition, the concrete may experience drying-shrinkage cracking due to its own self-desiccating properties (even with minimal evaporative moisture losses).
As a result, extreme care is required to protect the concrete (after its initial placement and subsequent finishing operations) from moisture loss and/or to add moisture to the concrete (to counteract the self-desiccation tendencies of the concrete). Certain types of moisture protection, such as liquid membrane curing agents, are degraded by ultraviolet radiation (i.e. sunlight) and/or foot- or vehicular-traffic. Other types of moisture protection, such as wet burlap or fog curing, require equipment and/or materials to remain on and/or adjacent to the concrete mass until such moisture protection is no longer necessary. Determining how long to maintain protection from moisture loss and/or providing additional moisture to the concrete mass is currently based on non-quantitative and inexact methods, such as specified minimum durations (such as the minimum seven-day water-cure required for bridge decks by the State of Oklahoma's Department of Transportation). These specified minimum durations are typically based on past experience with little or no relevance to the actual project conditions and/or concrete mix design being utilized.
Current “time-based” methods (such as the minimum seven-day water-cure required for bridge decks by the State of Oklahoma's Department of Transportation) for terminating moisture-loss protection of concrete are subject to numerous limitations. Two primary limitations are as follows:                1. Whereas the cementitious materials in concrete hydrate faster at higher temperatures, the use of a time-based method for determining protection from moisture loss experiences the same limitations as time-based strength-determinations. The disasters mentioned above highlight the inadequacies of such determinations. In essence, concrete subjected to higher temperatures will tend to require protection from moisture loss for a shorter duration than if it were subjected to lower temperatures. As such, the time should be “adjusted” based on the temperature-time history of the concrete. Properly applied, maturity methods can be used to meet this need.        2. Whereas the amount of cementitious material, types of cementitious materials, ratio of water to cementitious materials, etc. within a concrete mixture can have profound impacts on the hydration rate and self-desiccation properties of the concrete, a time-based approach simply cannot efficiently accommodate all the possibilities. A mix-specific calibration using maturity or enhanced maturity methods can be used to overcome this limitation.        
As such, an approach is desperately needed that can “adjust” the time requirement based on the properties of the concrete mix itself as well as the environmental conditions to which the concrete mass is ultimately subjected. Maturity and enhanced maturity methods (as discussed herein) can be employed to overcome these limitations.
The American Society for Testing and Materials (ASTM) developed a standard calibration procedure (ASTM C 1074) for predicting the compressive strength of concrete using strength-maturity relationship information and subsequent maturity calculations based on periodic temperature measurements. Each calibration curve is specific to a given mix design (i.e. the specific proportions and sources of the raw materials such as portland cement, fly ash, coarse aggregate, fine aggregate, etc.). As a part of the ASTM C 1074 standard practice, ASTM recommends two different methods for determining strength from maturity—Nurse-Saul and Arrhenius. The Nurse-Saul method relies upon a “datum temperature” as the basis for the maturity calculation, whereas the Arrhenius method relies upon an “apparent activation energy” value. ASTM C 1074 also provides recommended procedures for experimentally determining the datum temperature and/or apparent activation energy for the specific mix design for which strength-by-maturity determinations are desired.
The accuracy, repeatability and reproducibility of the ASTM C 1074 methods for determining datum temperature and apparent activation energy are less than optimum. In addition, whereas the cementitious hydration reactions occurring within a concrete mass result from many different cementitious reaction products, each of which has its own unique activation energy, the use of a single apparent activation energy and/or a single datum temperature to characterize the mix for all curing conditions may, at times, provide very unconservative prediction results. This is particularly so with the Arrhenius method, which is based on an exponential model for the maturity calculation as follows:
  M  =            ∑      0      t        ⁢          [                                    ⅇ                                          -                                                      E                    a                                    R                                            ·                              (                                                      1                                          T                      +                      273                                                        -                                      1                                                                  T                        ref                                            +                      273                                                                      )                                              ·          Δ                ⁢                                  ⁢        t            ]                      where        M=concrete maturity expressed as equivalent age (in hours or days)        e=natural logarithm constant (=2.7183)        Ea=apparent activation energy (in J/mole)        R=universal gas constant (−8.3144 J/(molexK))        T=average temperature (in ° C.) during time interval Δt        Tref=reference temperature (in ° C.)        Δt=length of time interval (in hours or days)        (NOTE: Sometimes the ratio EaIR is replaced by the term Q, which is simply the apparent activation energy divided by the gas constant, in Kelvin units.)        
Because the maturity calculation for the Arrhenius method relies upon an exponential model and because the apparent activation energy of the concrete mix is a part of the exponent, small variations in apparent activation energy can effectuate large changes in the calculated maturity value. This, in turn, can lead to substantial variations in the predicted strength values. At times, these variations may err on the conservative side. However, at other times these variations may be unconservative and, as such, may lead to unsafe conditions (e.g. removal of formwork or falsework before the concrete has achieved the necessary strength to support its own weight). Unfortunately, the apparent activation energy for the mix cannot be precisely determined ahead of time and the apparent activation energy can vary throughout the curing process (as different cementitious reaction products are used up and others are created) and/or throughout the life of a project (as cementitious materials with differing chemical compositions and/or other quality characteristics may be used throughout the life of a construction project, even when the materials are received from the same supplier and same manufacturing facility). This uncertainty about the “true” apparent activation energy of the mix creates a situation wherein one cannot know whether the corresponding maturity calculations are conservative or unconservative and, subsequently, whether the strength predictions based on those maturity calculations are conservative or unconservative.
In a similar, but less severe, fashion, the Nurse-Saul method can, at times, be unconservative. The impact is usually less severe due to the fact that the Nurse-Saul method assumes a linear rather than exponential relationship between temperature and cementitious reaction rates. The Nurse-Saul equation is as follows:
  M  =            ∑      0      t        ⁢          [                                    (                          T              -                              T                o                                      )                    ·          Δ                ⁢                                  ⁢        t            ]                      where        M=concrete maturity expressed as temperature-time factor (TTF) (in ° C.-Hours)        T=average temperature (in ° C.) during time interval Δt.        To=datum temperature (in ° C.)        Δt=length of time interval (in hours)        
The unconservative potential of conventional maturity calculations both for Arrhenius and Nurse-Saul methods is shown in Table 1 (where unconservative is defined as having an equivalent age factor, or EAF, higher than the “true” EAF).
Equivalent age represents the “age” of a mass of concrete expressed in terms of the actual age (in actual hours or days) of a separate, but similar, mass of concrete cured at a reference temperature. Two concrete masses having the same equivalent age are said to be equivalent in terms of the degree of cementitious hydration that has occurred within each mass. This expression of concrete maturity is most commonly associated with the Arrhenius method for determining concrete strength from maturity. However, the Nurse-Saul equation can be rearranged so as to equate the Nurse-Saul maturity value to an equivalent age or equivalent age factor (Carino and Lew 2001). Equivalent Age Factor, or EAF, refers to the factor, or multiplication value, necessary to convert the actual age of a mass of concrete, cured at temperatures other than the reference temperature, to its equivalent age. If the mass of concrete has been constantly cured at the reference temperature, its equivalent age factor will be one and its equivalent age will equal its actual age. If, on the other hand, the concrete has been cured at temperatures higher than the reference temperature, the equivalent age factor will be greater than one and its equivalent age will be greater than its actual age. For instance, if EAF=2.0, the concrete is presumed to be gaining strength twice as fast as concrete cured at the reference temperature. As such, if a concrete mass is cured at a constant temperature corresponding to an EAF=2.0, it is presumed to have reached two days' strength in one day, where “two days' strength” is the strength achieved in two days by similar concrete cured at the reference temperature.
As can be seen in Table 6, if the “true” apparent activation energy of the mix is relatively high (e.g. Q=6500 K, corresponding to Ea=54 kJ/mol), Arrhenius maturity calculations performed using lower activation energies are unconservative at lower temperatures (as shown graphically in FIG. 11), as is the Nurse-Saul method in this instance (where the reference temperature Tref is 50° C. and a datum temperature To of −10° C. is utilized) (as shown graphically in FIG. 12). Table 6 further demonstrates that, if the “true” apparent activation energy is relatively low (e.g. Q=3500 K, corresponding to Ea=29 kJ/mol), then Arrhenius maturity calculations performed using higher activation energies are unconservative at higher temperatures (as shown graphically in FIG. 13). Whereas the “true” apparent activation energy for a given mix is difficult to measure and can possibly change over time, it can be potentially dangerous to rely upon conventional maturity calculations (whether based on Arrhenius or Nurse-Saul) across the range of temperatures and conditions to which a mass of curing concrete might be exposed. Improved Maturity, as discussed herein, overcomes this limitation.